**WARNING: HUGE *** WALL OF TEXT INCOMING. NUMBERS/TESTING IS INCLUDED.**
*Credit for this goes to ***Beltenebros of Remora**
Why the Hagun is worth every penny:

For those with a short-attention span, here are calculated Weaponskill damages against a Greater Colibri (lvl 81 mob, vit 67, def 322) Reading the post in full will explain how I arrived at these numbers.

Hagun @ 100% TP: low 385, high 642

Other Great Katana @ 100% TP: low 336, high 560

Hagun @ 200% TP: low 513, high 855

Other Great Katana @ 200% TP: low 402, high 670

And, for fun, WS damages against Kirin (lvl 91, vit 120, def 413)

Hagun @ 100% TP: low 294, high 441

Other Great Katana @ 100% TP: low 258, high 387

Hagun @ 200% TP: low 393, high 589.5

Other Great Katana @ 200% TP: low 309, high 463.5

In other words, at 100TP against a Greater Colibri a Hagun can land a WS (without crit/double attack) for 80+ damage more than any competing Great Katana (Onimaru, Shinsoku, etc) and at 200TP it adds 185 damage more to the basal equations. These are rough numbers, not taking into account fluctuations based on landing a Critial Hit WS or Double Attacking, which will skew the numbers even further in the Hagun’s favor.

Really, the bottom line is that neither Onimaru, Ushikimaru, or Shinsoku increase base dmg by a larger % than Hagun increases fTP. Why is this important? Because- as a Samurai- the percentage of your Total (melee & WS) damage coming from WS, is almost ALWAYS going to be higher than the percentage of your total damage that you gain through melee strikes. In fact, your WS damage will probably be closer to 60%-80% of your total damage depending on what you fight, whether or not you use 6-hit, and whether or not you forget to meditate. We're not MNKs. Melee DoT is not a concern for SAM. To put it bluntly: if the Percentage of your Total Damage output coming from melee strikes instead of WS is high enough for ushikirimaru's base dmg to beat hagun's TP bonus, one has to really, truly fail as a SAM (hold TP too long, never meditate, not use any WS macro swaps, etc)

If you don't feel like reading further, the gist of what I'm going to try and demonstrate is that the higher damage on Weapon Skills provided by Hagun pulls it far ahead of the higher base damage afforded by other “competing” Great Katanas. I won't blame you for being suspicious of this statement, so read on from this point if you’d like to see how I arrived at it.

* * * * *

The Hagun looks like a boat oar and at first blush it's stats are unimpressive at best:

Hagun DMG:75 Delay:450 TP Bonus

In fact, compared to the Kazaridachi (the Great Katana most SAM used to ~71ish) it actually has a *lower* base damage, and it doesn't give you the sweet CHR +2 mod

Kazaridachi DMG:76 Delay:450 CHR+2

So, what gives? Why are Samurai across servers paying millions and millions of gil for a weapon that looks horrible and has lol base damage? Aren't the Onimaru (DMG: 77 / latent: DMG 83 att+18 acc +5) , Ushikirimaru (DMG:82 STR +2 HP +15) or Shinsoku (DMG:80 STR +5) superior choices?

In a word, no. And here's why

Weapon Skills and gaining TP for Weapon Skills are the two things Samurai were put on Vana'diel to do. The final three WS that a non-relic SAM learns (Tachi: Yukikaze, Tachi: Gekko, and Tachi: Kasha) all have two things in common. First, they have all have a modifier of STR: 75% (meaning, as I hope you should know, 75% of your Strength is factored in to your weapon's base damage during WS damage calculation) making STR the obvious stat to increase for WS gearswaps. Secondly, they share ridiculously high fTP Damage modifiers. To wit... 100%TP 1.5625

200%TP 1.875

300%TP 2.50

Compared to, say, Asuran Fists (with a fTP damage modifier of 1.00 for 100%, 200%, or 300% TP), Penta Thrust (same), Hexa Strike (you guessed it, fTP of 1.00 for all!), Dancing Edge (fTP of 1.875 regardless of TP) and other commonly seen WSes this is a HUGE variance for ths the fTP modifier.

So what's this have to do with the Hagun, you may be asking? Let's revisit the item's description again:

Hagun DMG:75 Delay:450 TP Bonus

The Hagun is from the "Martial" series of weapons and as such it will add 100% TP to your WS's fTP modifier the second you execute it. In other words, when you WS at 100% TP with your Hagun, you're effectively WSing at 200% TP. WS at 200% TP, and you’re really WSing at 300%TP... which where the millions of gil start to come into play. Depending on the mob you’re fighting the Hagun will add 2-300 damage to Yukikaze, Gekko, or Kasha which makes it drool-inducing for Samurai regardless of the sub (contrary to popular opinion: this makes it a *better* choice for SAM/THF despite the deceptively low base damage)

But what the hell is fTP anyway and how does that affect my Weapon Skill damage? I’m so glad you asked, because here comes the math!

The simplified version of the accepted non-Magic Weapon Skill Damage Equation is as follows:

Weapon Skill Damage = WSD * PDIF = (( D + fSTR + WSC) * fTP) * PDIF

where...

WSD: Base Weapon Skill Damage

PDIF: Function of the difference between your Attack vs. Mob's Def (ATT vs DEF)

D: Weapon's base damage

fSTR: Function of the difference between your STR and the mob's VIT.

WSC: Secondary Attribute Modifiers (STR +75% for SAM)

fTP: TP Multiplier of your WS

fStr: is bizarre and is essentially your Strength minus the mob’s Vit +4/4 (for merit-level mobs). Further, this "caps" at 8+(Weapon Damage/9) So, for a weapon with 75 damage, the cap is 16.

WSC: This value isn’t simply added. You take your base score, multiple it by the relevant percentage for the modifier (75% for STR) and then multiply it by a fixed integer based on your level (.83 for level 75) Oddly, the higher level you are the less impact modifiers have on your WS damage... although, this amount is almost inconsequential.

PDIF: Explaining PDIF calculations extensively would make this post even more of a Wall of Text than it already is, but suffice it to say that it can be easily calculated for melees by

(Your ATT / Mob’s DEF) with a level correction of 0.050 x every level the mob has over you (6, in this example) It’s worth noting that Tachi Yuki, Gekko, and Kasha all have mysteriously high PDIF values meaning you do more damage than you technically *should* be able to using the PDIF graph. When using Y/G/K it’s almost a given that your PDIF value will higher than normal. This further increases your overall damage % from Weapon Skills over melee strikes. Although conjecture, many SAM concerned with such things believe the level correction modifier does not apply to y/g/k. Anyway, this this ratio gives you your ratio of what to expect for a min and maximum PDIF value.

* * * * *

To put this rather involved equation into practice, I’ll illustrate exactly how much the Hagun brings to the table by way of an example.

Every good Weapon Skill needs a Hero! So for this example, let's take a look at our Hero in his WS Gear: A striking lvl 75 Elvaan SAM with a Hagun (that handsome devil!) with a total STR of 128 (food buff incl.) and a standard buffed attack of 502. The mob for this example is a pink, flying whipping boy- a merit standard Greater Colibri- which is accepted to have a lvl of 81, a VIT of 67 and a Defense of 322.

With that in mind, our hero approaches the Colibri with 100TP, draws his Hagun, and fires off a Tachi: Yukikaze. Zounds! Damage!

What we're going to calculate first is the WSD and then multiply that by the PDIF. For the WSD, we need to look at ((D + fSTR +WSC) *fTP) Please note fTP is not arithmetic, it is a MULTIPLIER, this is where the Hagun really shines since it is an exponential increase. At 100TP we can expect WSD of

Hagun ((75 + 16 + 80) * 1.875 ) = 321

Other Great Katana ((83 + 16 + 80) * 1.5625) = 280

Now, at 200TP the gap broadens...

Hagun ((75 + 16 + 80)* 2.50) = 427.5

Other Great Katana ((83 + 16 + 80) * 1.875 ) = 335

When we multiply these WSDs by the PDIF values of 1.2 and 2 we can expect to see...

Hagun @ 100% TP: low 385, high 642

Other Great Katana @ 100% TP: low 336, high 560

Hagun @ 200% TP: low 513, high 855

Other Great Katana @ 200% TP: low 402, high 670

It should be noted that you can’t WS at a value greater than 300%TP so if you ever go above 200TP on a Hagun you’re effectively wasting your damage potential. At 300TP, a Great Katana with a higher base damage will put out better numbers than a Hagun. For this reason many Samurai (our Hero included) carry around a Great Katana with a higher base damage (onimaru, etc) for those instances such as Kirin and the Shinjin when you have the luxury of building up to 300TP before the fight. Fire off your first WS with the higher base damage weapon, then switch back to the Hagun. It's really that simple.